Illustration with Python Central Limit Theorem | sample size increases the probability that sample mean is further from population mean than error

sampleSizeIncreaseLine.py

import numpy as np
import random
import matplotlib.pyplot as plt

# Step 1
## show that as the sample size increases the mean of sample is close to population mean
# build gamma distribution as population
shape, scale = 2., 2.  # mean=4, std=2*sqrt(2)
mu = shape*scale # mean
s = np.random.gamma(shape, scale, 1000000)
# margin of error
epsilon = 0.05

# Step 2
# list of probability of each sample size
proberror = []
# sample size for plotting
samplesize = []

# for each sample size
for n in range(100,10101,500): 
    # start count
    c = 0
    for i in range(0,100):
        # sample n sample
        rs = random.choices(s, k=n)
        # calculate mean
        mean = sum(rs)/len(rs)
        # check if the difference is larger than error
        if abs(mean - mu) > epsilon:
            # if larger count the sampling
            c += 1
    # Step 3
    # calculate the probability
    proberror.append(c/100)
    # save sample size for plotting
    samplesize.append(n)

# Step 4
# set figure size.
plt.figure(figsize=(20,10))
# plot each probability.
plt.plot(samplesize,proberror, marker='o')
# show plot.
plt.show()